Symmetry methods and space group representations in the theory of phase transitions

Abstract

A review is presented of main results of the phenomenological theory of phase transitions obtained by means of irreducible representations (IR) of the space symmetry groups. A geometrical method for obtaining low-symmetry phases as well as a scheme of a thermodynamical analysis of phase transitions consistent with this method are described. Basic principles are expounded of construction and analysis of the phase diagrams for multicomponent order parameters. It has been established that, even if the Lifshitz condition is satisfied, there may be some symmetry-related reasons giving rise to incommensurate phases near the multicritical point, phase diagrams are presented typical of this case. The role of external, symmetry-breaking fields has been analyzed. It has been shown on the basis of the general symmetry principles that a certain domain structure may exist on an ideal crystal surface. The structure of low-symmetry phases has been described using the notion of complete condensate of order parameters, a connection between this approach and that based on the theory of color symmetry has been discussed.